The calorie count of a serving of food can be computed based on its composition of carbohydrate, fat, and protein. the calorie count c for a serving of food can be computed using the formula upper c equals 4 h plus 9 f plus 4 p, where h is the number of grams of carbohydrate contained in the serving, f is the number of grams of fat contained in the serving, and p is the number of grams of protein contained in the serving. a serving of raisins contains 148 calories and 29 grams of carbohydrate. if raisins are a fat-free food, how much protein is provided by this serving of raisins?

Aparticle of mass m is projected with an initial velocity v0 in a direction making an angle α with the horizontal level ground as shown in the figure. the motion of the particle occurs under a uniform gravitational field g pointing downward. (a) write down the lagrangian of the system by using the cartesian coordinates (x, y). (b) is there any cyclic coordinate(s). if so, interpret it (them) physically. (c) find the euler-lagrange equations. find at least one constant of motion. (d) solve the differential equation in part (c) and obtain x and y coordinates of the projectile as a function of time. (e) construct the hamiltonian of the system, h, and write down the hamilton’s equations (canonical equations) of motion.

Abucket full of water weights 4 kg and water well is 10m deep. a girl draws water from the well. it takes the girl 3 minutes to draw a bucket full of water from the well. what is the power of the girl?

An electron is traveling with initial kinetic energy k in a uniform electric field. the electron comes to rest momentarily after traveling a distance d. (a) what is the magnitude of the electric field